South Yorkshire Police said they were arrested for a number of offences including public order.
Officers also issued 35 dispersal orders to fans deemed at risk of causing or becoming embroiled in disorder.
They were banned from certain areas and anyone found breaching them faced arrest.
Nine pubs also closed early yesterday because of disorder or concerns that violence between rival fans could have flared.
The game between Sheffield Wednesday and United, at Hillsborough, was the first in over five years.
Chief Superintendent Shaun Morley, Sheffield's District Commander, said: “Yesterday's large-scale police operation has seen a number of officers working to manage and police the Sheffield derby football match.
“The operation required coordination from a number of local authority partners, transport services, football clubs and teams from across the force, who all worked together to make yesterday possible.
“The overall purpose of this work was to ensure the event ran successfully and members of the public were kept safe. These aims were achieved and I would personally like to thank everyone for their involvement. I would also like to thank and acknowledge all of the fans who cooperated with us throughout the day and allowed us to do our job.
“There were a small minority of individuals who came intent on causing disruption and action was taken to address and prevent this type of behaviour.
“Over the course of the operation we have made 11 arrests for a variety of offences including public order, issued 35 Dispersal Orders and worked with a number of licensed premises, which saw nine public houses voluntarily close. This action was taken to avert disorder across the city and send out a clear message that violence will not be tolerated.
“I would like to thank all of the officers for their hard work and dedication as they made the whole operation possible. I hope the match was enjoyed by everyone and that our high visibility presence provided reassurance. Our main priority remains keeping the people of South Yorkshire safe and we will always work to achieve this.”